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A mode-dependent energy-based damage model for peridynamics and its implementation

Willberg, Christian and Wiedemann, Lasse and Rädel, Martin (2019) A mode-dependent energy-based damage model for peridynamics and its implementation. Journal of Mechanics of Materials and Structures, 14 (2), pp. 193-217. Mathematical Sciences Publishers (MSP). doi: 10.2140/jomms.2019.14.193. ISSN 1559-3959.

[img] PDF - Postprint version (accepted manuscript)

Official URL: https://msp.org/jomms/2018/13-3/


The mathematical modeling of failure mechanisms in solid materials and structures is a long standing problem. In recent years, peridynamics has been used as a theoretical basis for numerical studies of fracture initiation, evolution and propagation. In order to investigate damage phenomena numerically, suitable material and damage models have to be implemented in an efficient numerical framework. This framework should be highly parallelizable in order to cope with the computational effort due to the high spatial and, depending on the problem, temporal resolution required for high accuracy. The open-source peridynamic framework Peridigm offers a computational platform upon which new developments of the peridynamic theory can be implemented. Today, isotropic material models and a very simple damage model are implemented in Peridigm. This paper proposes three energy-based damage criteria. The implementation approach as well as the extension of Peridigm with these physically motivated models is described. The original criterion of Foster et al. is adapted for ordinary state based material. The other two criteria utilize the decomposition of peridynamic states in isotropic and deviatoric parts to account for the failure-mode dependency. The original criterion is verified by the numerical simulation of two mechanical problems. At first, a virtual double cantilever beam (DCB) experiment is performed to determine the energy release rate. This value is the fundamental material property required for the proposed criteria. Additionally, the DCB problem is then used to investigate the convergence of the numerical scheme implemented in Peridigm. In a second step, a model of a plate with a cylindrical hole under tensile loading is compared with an extended finite element method solution. Results of both numerical solutions are in good agreement. Finally, a fiber reinforced micro structure model is used to analyze the effect of the different criteria to the damage initiation and crack propagation under a more complex loading condition.

Item URL in elib:https://elib.dlr.de/127647/
Document Type:Article
Title:A mode-dependent energy-based damage model for peridynamics and its implementation
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Willberg, ChristianChristian.Willberg (at) dlr.dehttps://orcid.org/0000-0003-2433-9183
Wiedemann, LasseLasse.Wiedemann (at) dlr.deUNSPECIFIED
Rädel, Martinmartin.raedel (at) dlr.deUNSPECIFIED
Journal or Publication Title:Journal of Mechanics of Materials and Structures
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:Yes
DOI :10.2140/jomms.2019.14.193
Page Range:pp. 193-217
Publisher:Mathematical Sciences Publishers (MSP)
Keywords:Peridynamics, open source, fracture mechanics, composites
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:fixed-wing aircraft
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Simulation and Validation (old), E - Wind Energy (old)
Location: Braunschweig
Institutes and Institutions:Institute of Composite Structures and Adaptive Systems > Structural Mechanics
Deposited By: Willberg, Dr.-Ing. Christian
Deposited On:17 Jun 2019 10:00
Last Modified:11 Mar 2020 18:42

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